The influence of thermal blooming on the quality of an array of Hermite–Gaussian (H-G) beams propagating in the atmosphere is studied, where the incoherent combination is considered. An analytical expression of the equivalent distortion parameter of such an array is derived and validated. As the mode order or the inverse radial fill factor of an array of H–G beams increases, the thermal blooming effect weakens, requiring more time to reach steady-state thermal blooming. The focal shift of an array of H-G beams in the atmosphere is also investigated. Owing to the thermal blooming effect in the atmosphere, the actual focus moves away from the geometric focus as the mode order decreases, which is different from the behavior in free space. Additionally, for an array of multimode beams, the actual focus moves away from the target as the weighting factor of T E M 00 increases.

In 2000, Nikishov et al. presented an analytical model for the power spectrum of oceanic turbulence, in which the stable stratification of seawater is assumed, i.e., the eddy diffusivity of temperature is equal to that of salinity, and the eddy diffusivity ratio is equal to unity. Until now, all previous studies on the light propagation through oceanic turbulence were based on the Nikishov's power spectrum model. However, the eddy diffusivity of temperature and eddy diffusivity of salt are different from each other in most of underwater environments. Very recently, Elamassie et al. established a more reasonable power spectrum model of underwater turbulent fluctuations as an explicit function of eddy diffusivity ratio. The characteristic parameters such as the spatial coherence length of optical wave in turbulent medium play an important role in characterizing the strength of turbulence, the phase correction techniques in light propagation, etc. In the present paper, based on the Elamassie's power spectrum model of oceanic turbulence, the analytical formulae of the wave structure function, the spatial coherence length of optical wave and the Fried parameter in oceanic turbulence are derived, and the correctness of each of these formulae is verified. It is shown numerically that the results obtained by using the Elamassie's power spectrum model are quite different from those obtained by using the Nikishov's power spectrum model. If the Nikishov's power spectrum model is adopted, the strength of turbulence is underestimated when oceanic turbulence is dominated by the temperature fluctuations, while the strength of turbulence is overestimated when oceanic turbulence is dominated by the salinity fluctuations. If the Elamassie's power spectrum model is adopted, it is shown that the Kolmogorov five-thirds power law of the wave structure function is also valid for oceanic turbulence in the inertial range, and 2.1 times the spatial coherence length of optical wave is the Fried parameter, which are in agreement with those in atmospheric turbulence. In addition, based on the Elamassie's power spectrum model, the semi-analytical formula of the short-term beam spreading of Gaussian beams is derived in this paper, and its correctness is also verified. It is shown that the difference in short-term beam spreading is very large, whether the stable stratification of seawater is assumed or not. The results obtained in this paper are very useful for applications in optical communication, imaging and sensing systems involving turbulent underwater channels.

No abstract

Wavelength selection has a major impact on spectral beam combining (SBC) of laser beams that propagate in free space and in the atmosphere. We derive analytical expressions for the intensity and four characteristic quality parameters of free-space SBC beams. We show that the peak intensity, the mean-square beam width, and the M2 factor of an SBC beam at the target are all larger than those of one single laser beam of the same power and average wavelength. The peak intensity can be made higher by increasing the wavelength spacing but reducing the mean wavelength. However, when an SBC laser beam propagates in the atmosphere, the beam quality depends on the absorption coefficient of the multi-wavelength field due to thermal blooming. A thermal distortion number is introduced for an SBC beam and its validity is confirmed. We show that the power proportion of a high-absorption element within an SBC beam should be as low as possible to reduce the thermal blooming effect.